A method for determining exact solutions to a class of nonlinear models based on introduction of differential constraints

DOI10.1063/1.530439zbMath0813.35088OpenAlexW2007444025MaRDI QIDQ4317976

Domenico Fusco, Natale Manganaro

Publication date: 29 January 1995

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530439

zbMATH Keywords

hodograph transformationpartial differential equations of first orderflows in fluid-filled elastic tubes

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Bulk waves in solid mechanics (74J10) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Solutions to PDEs in closed form (35C05)

Related Items (4)

Generalized Riemann problems and exact solutions for \(p\)-systems with relaxation ⋮ Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs ⋮ Riemann problems and exact solutions to a traffic flow model ⋮ Exact solutions to a nerve pulse transmission model via a reduction procedure

Cites Work

• Linearization of a hyperbolic model for non-linear heat conduction through hodograph-like and Bäcklund transformation
• Linearization of nonautonomous models describing fluid filled elastic tubes and nonlinear elastic rods with variable cross-section
• Group analysis and constitutive laws for fluid filled elastic tubes
• Similarity representation of wave propagation in a nonlinear viscoelastic rod on a group theoretic basis
• On a class of quasilinear hyperbolic reducible systems allowing for special wave interactions
• On the introduction of viscoelasticity into one-dimensional models of arterial blood flow
• Symmetry and explicit solutions of partial differential equations
• Some exact solutions for wave propagation in viscoelastic, viscoplastic and electrical transmission lines
• The construction of special solutions to partial differential equations
• Similarity solutions to some non-linear impact problems
• Group-Invariant Solutions of Differential Equations
• A class of linearizable models and generation of material response functions to nonlinear hyperbolic heat conduction

This page was built for publication: A method for determining exact solutions to a class of nonlinear models based on introduction of differential constraints